Scottish striker Hardie, signed from Plymouth Argyle for the Red Dragons' long-awaited return to English football's second tier this season, poked home from close range after being introduced as a substitute at halftime.
Hardie's 66th-minute strike doubled the visitors' advantage after Tom O'Connor opened the scoring with a neat first-half finish in front of 37,020 fans at Marvel Stadium.
George Evans rounded out the scoring when his long-range shot squeezed under Victory's substitute goalkeeper Daniel Graskoski, and played up to the local crowd with his celebration by sticking out two fingers like an AFL goal umpire.
Wrexham manager Phil Parkinson was particularly pleased with Hardie's shift and brushed off injury concerns after the former Rangers man was taken off for the final few minutes.
"(It was) nothing really. He just got a bang and went a bit dizzy, and with four minutes to go there's no need to take a risk with him," Parkinson said.
"We're equally delighted for him to get a goal and that's what he's all about - movement in the opposition penalty box.
"He timed his run great and did what all good strikers do, gets those tap-ins in and around the six-yard box."
A youthful Victory outfit was far from disgraced, with Louis D'Arrigo going closest to finding the net when his volley rattled the crossbar soon after halftime.
Brazilian winger Santos went close to opening the scoring but was denied by Wrexham goalkeeper Arthur Okonkwo, and was then substituted with concussion caused by a ball to the head before halftime.
Victory boss Arthur Diles felt his younger players in particular would benefit from the experience of facing an English Championship outfit ahead of the Australia Cup tie against Olympic Kingsway on July 29.
"One thing that's very hard to emulate is, as a young player, being ready to play at AAMI Park for Melbourne Victory in front of thousands of people," Diles said.
"It's not easy and the fact that they can get that exposure, although it's a friendly match, it's a big thing for their development as young men and young footballers."
The friendly was a step for Wrexham towards their first season in England's second tier since 1982, after an unprecedented three consecutive promotions.
The club bought by Hollywood A-listers Ryan Reynolds and Rob Mac (formerly McElhenney) in 2021 will next face Sydney FC on Tuesday before completing their tour against Wellington Phoenix on July 19.
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